A common application in computer visualization is to virtually navigate inside a tubular structure in order to inspect its walls, such as in a virtual colonoscopy. In providing such navigation, it can be desirable to maintain an external view of the object such that one's position within the structure can be easily determined. This can be important when the structure being examined can look similar at different regions. However, using a typical 3D model for this purpose can lead to many problems. For instance, for a complex curving structure such as a colon, sections can occlude each other when they exist in the same region on the viewing plane and at different depths along the view direction. Such problems can necessitate rotation of the 3D structure.
Extracting a skeleton curve of an object is a popular method of compactly representing the general geometric shape of a structure. Significant work has been done to develop methods of extracting these skeleton curves. For example, skeleton extraction from volumetric medical data by connecting centerlines based on a medial voxel path is previously known using a distance from a boundary field with penalty weights to obtain general skeletons of treelike structures. Obtaining a skeleton directly from a mesh by contracting the surface, without any need for a volumetric representation, is also known. In addition, both surface and curve skeletons from genus zero structures have been extracted through the use of advection to move mass from the object's surface to its skeleton. The use of least squares optimization has been suggested for extracting curve skeletons in an efficient manner which can be insensitive to noise. It is also known that curve skeletons can be approximated for data from incomplete point clouds based on a generalized rotational symmetry axis for a set of points.
There are many uses for skeleton curves in the fields of computer graphics and visualization, and their 1D representation of 3D objects is useful for compact shape descriptions, navigation, animation, and analysis. Skeleton curves can be used to drive shape deformations. They have also been used in describing shape to allow for the creation of shape-based transfer functions. They can commonly be used for navigation in endoscopic visualizations, such as a virtual colonoscopy, where accurate curves can be important during the navigation.
A flattened representation of a structure can be useful for providing an overview of the entire structure in a single 2D view. Common methods of creating flattened representations straighten the object such that it can be difficult to locate where a position would correspond to in the actual tubular structure by simply looking at the flattened representation. This is evident, for example, in the case of flattening a virtual colon wall to a long linear strip. Though the 3D colon structure is often classified into separate sections based on the major bends it contains, this information can be lost in the flattened and straightened representation.
Thus, it may be beneficial to provide a 2D representation of a 3D tubular structure through the use of a skeleton representation that preserves the geometric context of the 3D structure in the 2D flattened representation such that the 2D flattened representation can be used to guide navigation within the structure, does not contain intersections which would cause occlusions, and overcomes at least some of the problems described above.